Finite Group DatabasebetaFinite Group Databasebeta| order | 20708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C167 · Schur multiplier (H2) = C2 |
| direct product | C2×D31×C167 |
| unambiguous semidirect product | C31⋊(C22×C167) |
| unambiguous semidirect product | (C2×C31)⋊(C2×C167) |
| Fitting, socle | C2×C31×C167 ⋊ C2 |
| derived, Sylow | C31 ⋊ C22×C167 |
| Hall | C31×C167 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C167 | D31 |
| commutator, cosocle, hypocenter | C31 | C22×C167 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C167 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C167 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10354 |
5678 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20708, 8);